Sampling Distributions and Hypothesis Testing: Terms and Concepts, Quizzes of Banking Law and Practice

Download Sampling Distributions and Hypothesis Testing: Terms and Concepts and more Quizzes Banking Law and Practice in PDF only on Docsity! TERM 1 Sampling Distribution Model DEFINITION 1 different random samples give different values for a statistic. The ________ shows the behavior of the statistic over all possible samples for the same size n. TERM 2 Sampling Variability/ Sampling Error DEFINITION 2 The variability we expect to see from one random sample to another. It is sometimes called _______, but _______ is the better term TERM 3 Sampling distribution model for a proportion DEFINITION 3 If assumptions of independence and random sampling are met, and we expect at least 10 success and 10 failures, then the sampling distribution of a proportion is modeled by a Normal model with a mean equal to the true proportion value, p, and a standard deviation equal to squrt(pq/n) TERM 4 Central Limit Theorem DEFINITION 4 The _________ states that the sampling distribution model of the sample mean (and proportion) from a random sample is approximately Normal for large n, regardless of the distribution of the population, as long as the observations are independent. TERM 5 Sampling Distribution Model for a mean DEFINITION 5 If assumptions of independence and random sampling are met, and the sample size is large enough, the sampling distribution of the sample mean is modeled by a Normal model with a mean equal to the population mean, mu, and a standard deviation equal to [sd/squrt(n)] TERM 6 Confidence Interval DEFINITION 6 A ________ for a model parameter is an interval of values usually of the form estimate +/- margin of error found from data in such a way that C% of all random samples will yield intervals that capture the true parameter value. TERM 7 One-proportion z-interval DEFINITION 7 A confidence interval for the true value of a proportion. The confidence interval is p-hat +/- z *SE(p-hat) where z* is a critical value from the Standard Normal model corresponding to the specified confidence interval TERM 8 Margin of Error DEFINITION 8 In a confidence interval, the extent of the interval on either side of the observed statistic value is called the ________. A ________ is typically the product of a critical value form the sampling distribution and a standard error from the data. A small _______ corresponds to a confidence interval that pins down the parameter precisely. A large ______ corresponds to a confidence interval that gives relatively little information about the estimated parameter. For a proportion, it = z* sqrt[(p-hat)(q-hat)/n] TERM 9 Critical Value DEFINITION 9 The number of standard errors to move away from the mean of the sampling distribution to correspond to the specified level of confidence. The ______, denoted z*, is usually found from a table or with technology. TERM 10 Null Hypothesis DEFINITION 10 The claim being assessed in a hypothesis test is called the _______. Usually, the _______ is a statement of "no change from the traditional value," "no effect," "no difference," or "no relationship." For a claim to be a testable _______, it must specify a value for some population that can form the basis for assuming a sampling distribution for a test statistic. TERM 21 Type II Error DEFINITION 21 the error of failing to reject a null hypothesis when in fact it is false (also called a "false negative"). The probability of a ______ error is commonly denoted as beta and depends on the effect size. TERM 22 Power DEFINITION 22 The probability that a hypothesis test will correctly reject a false null hypothesis is the _______ of the test. To find ______, we must specify a particular alternative parameter value as the "true" value. For any specific value in the alternative, the ______ is 1 - beta. TERM 23 Effect Size DEFINITION 23 The difference between the null hypothesis value and true value of a model parameter is called the ______ TERM 24 Variances of Independent random variables add DEFINITION 24 The variance of a sum or difference of independent random variables is the sum of the variances of those variables. TERM 25 Sampling Distribution of the difference between two proportions DEFINITION 25 The sampling distribution of (p-hat)1 - (p-hat)2 is, under appropriate assumptions, modeled by a Normal model with mean mu = p1-p2 and standard deviation SD(phat1 - phat2) = squrt (p1q1/n1 + p2q2/n2) TERM 26 Two-proportion z-interval DEFINITION 26 A _______ gives a confidence interval for the true difference in proportions, p1 - p2, in two independent groups. The confidence interval is (phat1 - phat2) +/- z* X SE(phat1 - phat2), where z* is a critical value form the standard Normal model corresponding to the specified confidence level TERM 27 Pooling DEFINITION 27 When we have data from different sources that we believe are homogeneous, we can get a better estimate of the common proportion and its standard deviation. We can combine, or _______, the data into a single group for the purpose of estimating the common proportion. The resulting _______ standard error is based on more data and is thus more reliable (if the null hypothesis is true and the groups are truly homogeneous). TERM 28 Two-Proportion z-test DEFINITION 28 Test the null hypothesis H0: p1-p2 = 0 by referring the statistic z = (phat1 - phat2) / SE pooled (phat1 - phat2) to a standard Normal Model. TERM 29 Chi-Square Model DEFINITION 29 Chi-square models are skewed to the right. They are parametrized by their degrees of freedom and become less skewed with increasing degrees of freedom. TERM 30 Cell DEFINITION 30 A _______ of a two-way table is one element of the table corresponding to a specific row and a specific column. Table _______ can hold counts, percentages, or measurements on other variables, or they can hold several values. TERM 31 Chi-square statistic DEFINITION 31 The _______ can be used to test whether the observed counts in a frequency distribution or contingency table match the counts we would expect according to some model. It is calculated as ______= sigma (obs-exp)^2 / exp ________ differ in how expected counts are found, depending on the question asked TERM 32 Chi-square test of goodness-of-fit DEFINITION 32 A test of whether the distribution of counts in one categorical variable matches the distribution predicted by a model is called a test of ________ . In a _______, the expected counts come from the predicting model. The test finds a P-value form a chi-square model with n - 1 degrees of freedom, where n is the number of categories in the categorical variable. TERM 33 Chi-square test of homogeneity DEFINITION 33 A test comparing the distribution of counts for 2 or more groups on the same categorical variable is called a _______ . a chi-square _______ finds expected counts based on the overall frequencies, adjusted for the totals in each group under the (null hypothesis) assumption that the distributions are the same for each group. We find a P-value from a chi-square distribution with (#Rows - 1) X (#Columns - 1) degrees of freedom, where # Rows gives the number of categories and #Columns gives the number of independent groups TERM 34 Chi-square test of independence DEFINITION 34 A test of whether two categorical variables are independent examines the distribution of counts for one group of individuals classified according to both variables. A _______ finds expected counts by assuming that knowing the marginal totals tells us the cell frequencies, assuming that there is no association between the variables. This turns out to be the same calculation as a test of homogeneity. We find a P-value from a chi- square distribution with (#Rows - 1) X (#Columns - 1) degrees of freedom, where #Rows gives the number of categories in one variable and #Columns gives the number of categories in the other. TERM 35 Chi-Square Component DEFINITION 35 The _______ calculation are (observed - expected)^2 / expected found for each cell of the table TERM 46 Marginal Distribution DEFINITION 46 In a contingency table, the distribution of either variable alone is called the _______ . The counts or percentages are the totals found in the margins (last row or column) of the table. TERM 47 Conditional Distribution DEFINITION 47 The distribution of a variable restricting the Who to consider only a smaller group of individuals is called a _______ . TERM 48 Independence DEFINITION 48 Variables are said to be ______ if the conditional distribution of one variable is the same for each category of the other. TERM 49 Segmented Bar Chart DEFINITION 49 A _______ displays the conditional distribution of a categorical variable within each category of another variable. TERM 50 Simpson's Paradox DEFINITION 50 when averages are taken across different groups, they can appear to contradict the overall averages. TERM 51 Population DEFINITION 51 The entire group of individuals or instances about whom we hope to learn TERM 52 Sample DEFINITION 52 a (representative) subset of a population, examined in hope of learning about the population. TERM 53 Sample Survey DEFINITION 53 A study that asks questions of a sample drawn from some population in the hope of learning something about the entire population. Polls taken to assess voter preferences are common ______ TERM 54 Bias DEFINITION 54 Any systematic failure of a sampling method to represent its population is ______ . It is almost impossible to recover from _______ , so efforts to avoid it are well spent. Common errors include - relying on voluntary response - undercoverage of the population - nonresponse ______ - response _______ TERM 55 Randomization DEFINITION 55 The best defense against bias is ______ , in which each individual is given a fair, random chance of selection TERM 56 Sample Size DEFINITION 56 The number of individuals in a sample. The _______ determines how well the sample represents the population, not the fraction of the population sampled. TERM 57 Census DEFINITION 57 A sample that consists of the entire population TERM 58 Population parameter DEFINITION 58 a numerically valued attribute of a model for a population. We rarely expect to know the true value of a _______ , but we do hope to estimate it from sampled data. For example, the mean income of all employed people in the country is a _______ . TERM 59 Statistic, Sample Statistic DEFINITION 59 _______ are values calculated fro sampled data. Those that correspond to, and thus estimate, a population parameter, are of particular interest. For example, the mean income of all employed people in a representative sample can provide a good estimate of the corresponding population parameter. The term "sample statistic" is sometimes used, usually to parallel the corresponding term "population parameter." TERM 60 Representative DEFINITION 60 A sample is said to be ________ if the statistics computed from it accurately reflect the corresponding population parameters